For the Dough: Use a large bowl (or a stand mixer) and combine the warm milk and half of the white sugar together. Now sprinkle the yeast over the milk mixture and stir it to combine. Allow the yeast to sit for about 10 minutes, until it gets foamy/frothy looking.
After the yeast gets frothy, add in the rest of the white sugar, the eggs, the butter, vanilla extract, flour, and the salt. If you are using a stand mixer, place the dough hook attachment on and mix it on low speed until it forms a dough (about 2 minutes), and increase the speed to high for another 3-4 minutes. The dough should be pretty smooth but slightly tacky.
If you aren’t using a stand mixer, simply combine all of the ingredients until a dough forms, then knead the dough by hand on a floured surface for about 10 minutes.
Use your hands to shape the dough into a ball, and put it into a lightly greased bowl. Cover the bowl with a clean kitchen towel, or plastic wrap and place it in a warm place and allow it to rise for about one hour. Dough should proof, and double in size.
If you used instant or rapid rise yeast, you do not need to allow the dough to proof. Just continue with the instructions.
Making the cinnamon rolls: Use your hands to punch the air out of the proofed dough. Then place the dough out onto a clean and floured surface. Use a rolling pin to roll the dough out to about ½ inch thickness.
Make the filling: Use a spatula, spoon, or butter knife to spread the room temperature, softened butter over the dough. Leave about a ½ inch edge.
Now sprinkle the brown sugar, cinnamon, and salt over the butter. Then use the spatula to spread it out evenly over all of the rolls.
Start from the longest side and begin to roll the dough into a log. Roll it fairly tightly until you get to the other end. Pinch the seam to seal the dough into each other.
Use a sharp scraper, knife, or a piece of dental floss to cut the rolls into 1 ½ to 2 inch thick rolls. You should get about 12 cinnamon rolls. Add them into a 9x13 baking dish, and leave a little bit of space in between them.
Cover the baking dish with a towel or plastic wrap, and set them in a warm spot to rise for one hour. When they have puffed up again, its time to bake!
Preheat your oven to 350°F and place the unwrapped baking dish in the oven for about 30 minutes, or until they are golden brown. While the rolls are baking, make the icing.
Making the icing: Use a medium bowl (or stand mixer), and mix up the cream cheese and butter until they are smooth and creamy. Now add the powdered sugar and vanilla and mix until it is all fully incorporated and smooth.
When the rolls are done baking, spread the icing all over the top and smear it around to get it into every crevice. And enjoy!